Find all integer solutions to the equation $$\frac{xyz}{w}+\frac{yzw}{x}+\frac{zwx}{y}+\frac{wxy}{z}=4$$
Problem
Source: China Northern MO 2015 grade 10 p1 CNMO
Tags: number theory, Diophantine equation, diophantine
Source: China Northern MO 2015 grade 10 p1 CNMO
Tags: number theory, Diophantine equation, diophantine
Find all integer solutions to the equation $$\frac{xyz}{w}+\frac{yzw}{x}+\frac{zwx}{y}+\frac{wxy}{z}=4$$